1

Cosmology with Supernovae:Lecture 2

Josh Frieman

I Jayme Tiomno School of Cosmology, Rio de Janeiro, Brazil

July 2010

Hoje

• V. Recent SN Surveys and Current Constraints on Dark Energy

• VI. Fitting SN Ia Light Curves & Cosmology

• VII. Systematic Errors in SN Ia Distances

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Coming Attractions

• VIII. Host-galaxy correlations• IX. SN Ia Theoretical Modeling• X. SN IIp Distances• XI. Models for Cosmic Acceleration• XII. Testing models with Future Surveys:

Photometric classification, SN Photo-z’s, & cosmology

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Lum

inos

ity

Time

m15

15 days

Empirical Correlation: Brighter SNe Ia decline more slowly and are bluerPhillips 1993

SN Ia Peak LuminosityEmpirically correlatedwith Light-Curve Decline Rate and Color

Brighter Slower, Bluer

Use to reduce Peak Luminosity Dispersion:

Phillips 1993

Pea

k L

umin

osit

y

Rate of declineGarnavich, etal€

M ipeak = c i + f i(Δm15)

in rest - frame passband i

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Type Ia SNPeak Brightnessas calibratedStandard Candle

Peak brightnesscorrelates with decline rate

Variety of algorithms for modeling these correlations: corrected dist. modulus

After correction,~ 0.16 mag(~8% distance error)

Lum

inos

ity

Time

7

Published Light Curves for Nearby Supernovae

Low-z SNe:

Anchor Hubble diagram

Train Light-curve fitters

Need well-sampled, well-calibrated, multi-band light curves

Low-z Data

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9

Correction for Brightness-Decline relation reduces scatter in nearby SN Ia Hubble Diagram

Distance modulus for z<<1:

Corrected distance modulus is not a direct observable: estimated from a model for light-curve shape

€

m − M = 5logv

km/sec

⎛

⎝ ⎜

⎞

⎠ ⎟− 5log h +15

Riess etal 1996

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Acceleration Discovery Data:High-z SN Team

10 of 16 shown; transformed to SN rest-frame

Riess etal

Schmidt etal

V

B+1

Riess, etal High-z Data (1998)

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High-z Supernova Team data (1998)

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Likelihood Analysis

This assume

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€

−2ln L = χ 2 =(μ i − μmod (zi;Ωm ,ΩΛ,H0)2

σ μ ,i2

i

∑

Since μmod = 5log(H0dL ) − 5log(H0), let ˆ μ ≡ μmod (H0 = 70)

and define Δ i = μ i − ˆ μ . If we fix H0, then we are minimizing

ˆ χ 2 =Δ i

2

σ i2

i

∑

To marginalize over logH0 with flat prior, we instead minimize

χ mar2 = −2ln d(5logH0)exp −χ 2 /2( )∫

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥= ˆ χ 2 −

B2

C+ ln

C

2π

⎛

⎝ ⎜

⎞

⎠ ⎟,

where

B =Δ i

σ i2

i

∑ , C =1

σ i2

i

∑

σ μ ,i2 = σ μ , fit

2 + σ μ ,int2 + σ μ ,vel

2

Goliath etal 2001

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High-z SN Team Supernova Cosmology Project

1998-2010 SN Ia Synopsis• Substantial increases in both quantity and quality of SN

Ia data: from several tens of relatively poorly sampled light curves to many hundreds of well-sampled, multi-band light curves from rolling surveys

• Extension to previously unexplored redshift ranges: z>1 and 0.1<z<0.3

• Extension to previously underexplored rest-frame wavelengths (Near-infrared)

• Vast increase in spectroscopic data• Identification of SN Ia subpopulations (host galaxies)• Entered the systematic error-dominated regime, but

with pathways to reduce systematic errors

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Supernova Legacy Survey (2003-2008)

Megaprime Mosaic CCD camera

Observed 2 1-sq deg regions every 4 nights

~400+ spectroscopically confirmed SNe Ia to measure w

Used 3.6-meter CFHT/“Megacam”

36 CCDs with good blue response

4 filters griz for good K-corrections and color measurement

Spectroscopic follow-up on 8-10m telescopes

8 nights/yr:LBL/Caltech

DEIMOS/LRIS for types,

intensive study, cosmology with

SNe II-P

Keck

120 hr/yr: France/UK FORS 1&2 for types,

redshifts

VLT

120 hr/yr: Canada/US/UK

GMOS for types, redshifts

Gemini 3 nights/yr: Toronto

IMACS for host redshifts

Magellan

Spectra

SN Identification

Redshifts

Power of a Rolling Search

SNLS Light curves

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First-Year SNLS Hubble Diagram

SNLS 1st Year Results

Astier et al. 2006

Using 72 SNefrom SNLS+40 Low-z

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Wood-Vasey, etal (2007), Miknaitis, etal (2007): results from ~60 ESSENCE SNe (+Low-z)

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60 ESSENCE SNe72 SNLS SNe

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Higher-z SNe Ia from ACS

Z=1.39 Z=1.23Z=0.46 Z=0.52 Z=1.03

50 SNe Ia, 25 at z>1 Riess, etal

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(m

-M)

HST GOODS Survey (z > 1) plus

compiled ground-based SNe Riess etal 2004

Supernova Cosmology ProjectSN Ia Union Compilation Kowalski et al., ApJ, 2008

Data tables and updates at http://supernova.lbl.gov/Union

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€

−2ln Pposterior =(μ i − μmod (zi;w,Ωm,ΩDE )2

σ μ ,i2

i

∑ + χ BAO2 + χ CMB

2

where latter terms incorporate BAO and CMB priors :

BAO (SDSS LRG, Eisenstein etal 05) :

A(z1;w,Ωm,ΩDE ) =Ωm

E(z1)1/ 3

1

z1 Ωk

Sk Ωk

1/ 2 dz

E(z)0

z1

∫ ⎛

⎝ ⎜

⎞

⎠ ⎟

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥

2 / 3

with

χ BAO2 = [(A(z1;w,Ωm,ΩDE ) − 0.469) /0.017]2 for z1 = 0.35

CMB (WMAP5, Komatsu etal 08) :

R(zCMB ;w,Ωm ,ΩDE ) =Ωm

Ωk

Sk Ωk

1/ 2 dz

E(z)0

zCMB

∫ ⎛

⎝ ⎜

⎞

⎠ ⎟

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥

with

χ CMB2 = [(R(zCMB ;w,Ωm ,ΩDE ) −1.710) /0.019]2 for zCMB =1090

Likelihood Analysis with BAO and CMB Priors

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Recent Dark Energy Constraints

Improved SN constraints

Inclusion of constraints from WMAP Cosmic Microwave Background Anisotropy (Joana) and SDSS Large-scale Structure (Baryon Acoustic Oscillations; Bruce, Daniel)

Only statistical errors shownassuming w = −1

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Only statistical errors shown

assuming flat Univ. and constant w

SNLS Preliminary 3rd year Hubble Diagram

Conley et al, Guy etal (2010): results with ~252 SNLS SNe

Independent analyses with 2 light-curve fitters: SALT2, SiFTO

Results published from 2005 season

Frieman, et al (2008); Sako, et al (2008)

Kessler, et al 09; Lampeitl et al 09; Sollerman et al 09

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SDSS II Supernova Survey Goals• Obtain few hundred high-quality* SNe Ia light curves in the

`redshift desert’ z~0.05-0.4 for continuous Hubble diagram• Probe Dark Energy in z regime complementary to other

surveys• Well-observed sample to anchor Hubble diagram, train

light-curve fitters, and explore systematics of SN Ia distances

• Rolling search: determine SN/SF rates/properties vs. z, environment

• Rest-frame u-band templates for z >1 surveys • Large survey volume: rare & peculiar SNe, probe outliers of

population

*high-cadence, multi-band, well-calibrated

Spectroscopic follow-up telescopes

R. Miquel, M. Molla, L. Galbany

Search Template Difference

g

r

i

Searching For Supernovae• 2005

– 190,020 objects scanned– 11,385 unique

candidates– 130 confirmed Ia

• 2006– 14,441 scanned– 3,694 candidates– 193 confirmed Ia

• 2007 – 175 confirmed Ia

• Positional match to remove movers• Insert fake SNe to monitor efficiency

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SDSS SN PhotometryHoltzman etal (2008)

B.

Dild

ay

500+ spec confirmed SNe Ia + 87 conf. core collapse plus >1000 photometric Ia’s with host z’s

Spectroscopic Target Selection2 Epochs

SN Ia Fit

SN Ibc Fit

SN II Fit

Sako etal 2008

Spectroscopic Target Selection2 Epochs

SN Ia Fit

SN Ibc Fit

SN II Fit

31 Epochs

SN Ia Fit

SN Ibc Fit

SN II Fit

Fit with template library

Classification>90%accurate after 2-3 epochs

Redshifts 5-10% accurate

Sako etal 2008

SN and Host Spectroscopy

MDM 2.4mNOT 2.6mAPO 3.5mNTT 3.6mKPNO 4mWHT 4.2mSubaru 8.2mHET 9.2mKeck 10mMagellan 6.5mTNG 3.5mSALT 10m SDSS 2.5m

2005+2006Determine SN Type and Redshift

Spectroscopic Deconstruction

SN modelHost galaxy modelCombined model

Zheng, et al (2008)

Fitting SN Ia Light Curves

• Multi-color Light Curve Shape (MLCS2k2)

Riess, etal 96, 98; Jha, etal 2007

• SALT-II

Guy, etal 05,08

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€

mmodi (t − t0) = μ + M j (t − t0) + P j (t − t0)Δ + Q j (t − t0)Δ2

+ K ij (t − t0) + Xhostj (t − t0) + XMW

i (t − t0)

fit parameters

Time of maximum distance modulus host gal extinction stretch/decline rate

time-dependent model “vectors”

trained on Low-z SNe

∆ <0: bright, broad∆ >0: faint, narrow, redder

MLCS2k2 Light-curve Templatesin rest-frame j=UBVRI;built from ~100 well-observed, nearby SNe Ia

observedpassband

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Host Galaxy Dust Extinction

€

Aλ = −2.5logfobs(λ )

f true (λ )

⎛

⎝ ⎜

⎞

⎠ ⎟

€

Aλ

AV

= a(λ ) +b(λ )

RV

• Extinction:

• Empirical Model for wavelength dependence:

• MLCS: AV is a fit parameter, but RV is usually fixed to a global value (sharp prior) since it’s usually not well

determined SN by SN

Cardelli etal 89 (CCM)

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Host Galaxy Dust Extinction

Jha

Milky Way avg.

Historically, MLCS used Milky Way average of RV=3.1

Growing evidence that this doesn’t represent SN host galaxy population well

Extract RV by matching colors of SDSS SNe to MLCS simulations

• Use nearly complete (spectroscopic + photometric) sample

• MLCS previously used Milky Way avg RV=3.1

• Lower RV more consistent with SALT color law and other recent SN RV estimates

D. Cinabro

€

RV =AV

E(B −V )≈ 2

Carnegie Supernova Project: Low-z

n CSP is a follow-up project

n Goal: optical/NIR light-curves and spectro-photometry for

n > 100 nearby SNIa

n > 100 SNII

n > 20 SNIbc

n Filter set: BV + u’g’r’i’ + YJHK

n Understand SN physics

n Use as standard candles.

n Calibrate distant SN Ia sample

CSP Low-z Light Curves

Folatelli, et al. 2009Contreras, et al. 2009: 35 optical light curves (25 with NIR)

Varying Reddening Law?

Folatelli et al. (2009)

2005A2006X

Local Dust?

Goobar (2008): higher density of dust grains in a shell surrounding the SN: multiple scattering steepens effective dust law(also Wang)

Folatelli et al. (2009)

Two Highly Reddened SNe

Priors & Efficiencies

€

χMLCS2 =

Fidata − Fi

mod (t0,Δ,AV ,μ)[ ]2

σ i2

i

∑ − 2ln P(AV )P(Δ)ε(z,AV ,Δ)( )

Determine priors and efficiencies from data and Monte Carlo simulations

Priors & Efficiencies

Determine priors and efficiencies from data and Monte Carlo simulations

Inferred P(AV) Inferred P()

€

χMLCS2 =

Fidata − Fi

mod (t0,Δ,AV ,μ)[ ]2

σ i,phot2 + σ i,mod

2i

∑ − 2ln P(AV )P(Δ)ε(z,AV ,Δ)( )

Model Spectroscopic & Photometric Efficiency

Redshift distribution for all SNe passing photometric selection cuts (spectroscopically complete sample)

Data

Need to model biases due to what’s missing

Difficult to model spectroscopic selection

Model Selection Function

Include Selection Function

Monte Carlo Simulations match data distributions

Use recorded observing conditions (local sky, zero-points, PSF, etc)

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Show likelihood plots for MLCS

MLCS fit to one of the ESSENCE SNe

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prior

Marginalized PDFs

μ distribution approximated by Gaussian for cosmology fit

59MLCS Likelihood Contours for this object